On the Fourier Transform Related to the Diamond Klein - Gordon Kernel

Abstract

In this article, we study the fundamental solution of the operator $$\left((\diamond+m^2)\left(\frac{\triangle^2+\boxdot^2}{2}\right)\right)^{k}$$, iterated $k$-times and is defined by (\ref{odot}),where $m$ is a nonnegative real number, and $k$ is a nonnegative integer. After that, we study the Fourier transform of the operator $ \left((\diamond+m^2)\left(\frac{\triangle^2+\boxdot^2}{2}\right)\right)^{k}\delta$.